arXiv research

The paper analyzes early stopping in linear regression and shows it's equivalent to ridge regularization.

The paper studies RBSDEs with arbitrary stopping times and their solutions.

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller's) and long (buyer's) positions in an Americ…

New algorithm solves complex stopping problems with robust optimization.

In this paper, we provide a solution to two problems which have been open in default time modeling in credit risk. We first show that if $τ$ is an arbitrary random (default) time such that its Azéma's supermartingale $Z_t^τ=¶(τ>t|\F_t)$ is continuous, then $τ$ avoids stopping times. We then disprove a conjecture about …

The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) 906-925] from diffusion processes to arbitrary continuous semimartin…

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an optimal stopping problem with …

We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering …

CITE algorithm provides anytime-valid certification of model outputs.

This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price processes are quasi-left-continu…

Solves optimal stopping problem with Poisson constraints using jumps.

Continuous-time optimal stopping solved with deep reinforcement learning

A new sequential test for unnormalized densities.

New algorithms improve stopping time for best arm identification.

We consider the optimal double stopping time problem defined for each stopping time $S$ by $v(S)=\esssup\{E[ψ(τ_1, τ_2) | \F_S], τ_1, τ_2 \geq S \}$. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of …

Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Solves optimal stopping for Gauss-Markov bridges using time-space transformation.

We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The op…

In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.

Sharp risk bounds for early-stopping in Gaussian linear regression are derived.

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …

The paper tackles optimal stopping problems using reinforcement learning and singular control.

Early stopping method saves up to 75% computation time in policy search tasks.

Paper solves a complex stopping problem using regularization and HJB equations.

Method calculates Parisian stopping times and option prices using Markov chains.

Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.

Study optimal stopping times under regime-switching models with constraints.

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to cons…

The paper develops formulas for hedging and arbitrage in markets with random stopping times.

The Teichmüller harmonic map flow deforms both a map from an oriented closed surface $M$ into an arbitrary closed Riemannian manifold, and a constant curvature metric on $M$, so as to reduce the energy of the map as quickly as possible [16]. The flow then tries to converge to a branched minimal immersion when it can [1…

New method models stopping times that can be equal with non-zero probability.

We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time…

This paper considers a time-inconsistent stopping problem in which the inconsistency arises from non-constant time preference rates. We show that the smooth pasting principle, the main approach that has been used to construct explicit solutions for conventional time-consistent optimal stopping problems, may fail under …

Develops confidence bounds for off-policy evaluation in contextual bandits.

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…

Existence of strong randomized equilibria in mean-field games with common noise.

Early stopping improves sample quality in latent diffusion models.

Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Orn…

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $δ$, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…

A framework for robust exploration in reinforcement learning under ambiguity.

New algorithms use Gaussian processes to optimize stopping times in financial markets.

Probabilistic proof of smooth boundaries in optimal stopping problems.

Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time …

This work bounds the run-time of nonconvex optimization with early stopping.

Given an initial (resp., terminal) probability measure $μ$ (resp., $ν$) on $\mathbb{R}^d$, we characterize those optimal stopping times $τ$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_τ|^α$, $α> 0$, where $(B_t)_t$ is Brownian motion with initial law $B_0\sim μ$ and with final distribution --once stop…

We consider the problem of asynchronous online testing, aimed at providing control of the false discovery rate (FDR) during a continual stream of data collection and testing, where each test may be a sequential test that can start and stop at arbitrary times. This setting increasingly characterizes real-world applicati…